We propose a sure screening approach for recovering the structure of a transelliptical graphical model in the high dimensional setting. We estimate the partial correlation graph by thresholding the elements of an estimator of the sample correlation matrix obtained using Kendall's tau statistic. Under a simple assumption on the relationship between the correlation and partial correlation graphs, we show that with high probability, the estimated edge set contains the true edge set, and the size of the estimated edge set is controlled. We develop a threshold value that allows for control of the expected false positive rate. In simulation and on an equities data set, we show that transelliptical graphical sure screening performs quite competitively with more computationally demanding techniques for graph estimation.
翻译:我们提出一个可靠的筛选方法,以便在高维设置中恢复一个跨电子图形模型的结构。我们通过使用肯德尔的图伊统计数据对一个样本相关矩阵估计符的元素进行阈值来估计部分相关图形。根据对相关图和部分相关图之间关系的简单假设,我们显示,在概率很高的情况下,估计边缘集包含真实的边缘集,估计边缘集的大小得到控制。我们开发了一个临界值,以便控制预期的虚假正率。在模拟和股票数据集中,我们显示,在模拟和一组股票数据中,跨电子图形确实进行非常有竞争力的筛选,用更具有计算难度的图表估算技术进行更具有竞争力的筛选。